Scattering of antiplane waves by fluid-filled cracks

Abstract

Propagation of time-harmonic antiplane waves in an unbounded linearly-elastic solid containing parallel fluid-filled cracks is investigated. The viscous friction effects are represented by appropriate boundary conditions on the crack faces. The cracks are randomly distributed in a slab of finite thickness. Taking configurational averages over all crack configurations, one finds that the average motion in the solid is governed by two coupled integral equations. It is inferred from these equations that, inside the cracked region, there is a forward motion and a backward motion, which are described by a complex-valued wavenumber. Outside the cracked region, there are unattenuated reflected and transmitted wave motions, for which simple expressions are obtained. Numerical results are presented for the speed, attenuation, reflection and transmission in terms of the frequency, viscosity, crack density, angle of incidence and slab thickness